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Simplifying (1800x2) + -1(25x) + 0.008 = 0 Remove parenthesis around (25x) (1800x2) + -1 * 25x + 0.008 = 0 Multiply -1 * 25 (1800x2) + -25x + 0.008 = 0 Reorder the terms: 0.008 + -25x + (1800x2) = 0 Solving 0.008 + -25x + (1800x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1800 the coefficient of the squared term: Divide each side by '1800'. 0.000004444444444 + -0.01388888889x + x2 = 0 Move the constant term to the right: Add '-0.000004444444444' to each side of the equation. 0.000004444444444 + -0.01388888889x + -0.000004444444444 + x2 = 0 + -0.000004444444444 Reorder the terms: 0.000004444444444 + -0.000004444444444 + -0.01388888889x + x2 = 0 + -0.000004444444444 Combine like terms: 0.000004444444444 + -0.000004444444444 = 0.000000000000000 0.000000000000000 + -0.01388888889x + x2 = 0 + -0.000004444444444 -0.01388888889x + x2 = 0 + -0.000004444444444 Combine like terms: 0 + -0.000004444444444 = -0.000004444444444 -0.01388888889x + x2 = -0.000004444444444 The x term is -0.01388888889x. Take half its coefficient (-0.006944444445). Square it (0.00004822530865) and add it to both sides. Add '0.00004822530865' to each side of the equation. -0.01388888889x + 0.00004822530865 + x2 = -0.000004444444444 + 0.00004822530865 Reorder the terms: 0.00004822530865 + -0.01388888889x + x2 = -0.000004444444444 + 0.00004822530865 Combine like terms: -0.000004444444444 + 0.00004822530865 = 0.000043780864206 0.00004822530865 + -0.01388888889x + x2 = 0.000043780864206 Factor a perfect square on the left side: ((x) + -0.006944444445)((x) + -0.006944444445) = 0.000043780864206 Calculate the square root of the right side: 0.006616711 Break this problem into two subproblems by setting ((x) + -0.006944444445) equal to 0.006616711 and -0.006616711.Subproblem 1
(x) + -0.006944444445 = 0.006616711 Simplifying (x) + -0.006944444445 = 0.006616711 x + -0.006944444445 = 0.006616711 Reorder the terms: -0.006944444445 + x = 0.006616711 Solving -0.006944444445 + x = 0.006616711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = 0.006616711 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = 0.006616711 + 0.006944444445 x = 0.006616711 + 0.006944444445 Combine like terms: 0.006616711 + 0.006944444445 = 0.013561155445 x = 0.013561155445 Simplifying x = 0.013561155445Subproblem 2
(x) + -0.006944444445 = -0.006616711 Simplifying (x) + -0.006944444445 = -0.006616711 x + -0.006944444445 = -0.006616711 Reorder the terms: -0.006944444445 + x = -0.006616711 Solving -0.006944444445 + x = -0.006616711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = -0.006616711 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = -0.006616711 + 0.006944444445 x = -0.006616711 + 0.006944444445 Combine like terms: -0.006616711 + 0.006944444445 = 0.000327733445 x = 0.000327733445 Simplifying x = 0.000327733445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.013561155445, 0.000327733445}
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